display all the ideas for this combination of texts
1 idea
13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
From: William D. Hart (The Evolution of Logic [2010], 4) | |
A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |